The!force!feedback!device!chosen!for!the!purpose!of!this!study!was!a!Geomagic®!
Touch™! (formerly! known! as! Phantom®! Omni™! by! SensAble™).! This! is! a! haptic!
device,!which!makes!it!possible!for!users!to!touch!and!manipulate!virtual!objects.!It!
has! six! degrees! of! freedom! with! positional! sensing! and! uses! an! array! of! motor!
sensors! attached! on! a! mechanical,! robotic! arm! to! replicate! haptic! properties! of!
virtual!objects!in!the!real!world![89].!!
6.3.1 Rendering of Stiffness
One!of!the!most!common!ways!to!render!stiffness!in!virtual!environments!is!using!
Hooke’s!Law!(e.g.![90]!and![91]).!Hooke’s!law!is!an!easy!formula!to!implement!that!
gives!an!accurate!output!of!the!reaction!force!proportional!to!the!penetration!depth!
of!the!user!into!the!virtual!object!and!normal!to!the!surface!of!the!object.!!
The!equation!through!which!physical!stiffness!can!be!rendered!using!Hooke’s!Law!
is:!
! ! = −!"! (9.)!
In!this!formula,!the!force!F!is!calculated!by!multiplying!the!stiffness!constant!k!by!
the! displacement! vector! x.! When! simulating! contact! with! a! virtual! object,! forces!
that!resist!the!device!end!effector!from!penetrating!the!virtual!object’s!surface!must!
be!calculated.!!
The! way! virtual! stiffness! was! simulated! was! through! the! concept! of! a! cursor!
following!the!movement!of!tip!of!the!device’s!arm!in!the!virtual!environment!(see!
Figure!27,!circled!point).!When!the!cursor!comes!in!contact!with!a!virtual!object,!
the!coordinates!of!this!point!of!contact,!or!surface!contact!point!(SCP)!are!recorded.!
The!SCP!is!therefore!a!point!that!attempts!to!follow!the!endGeffector!position!(point!
at!the!end!of!the!arm)!but!is!stopped!by!the!surface!of!the!virtual!object.!!
The!force!is!then!calculated!by!simulating!a!spring!stretched!from!the!endGeffector!
position!to!the!SCP.!Figure!27!shows!penetration!into!the!object.!
More! specifically,! applying! Hooke’s! law! (see! equation! 15.),! x! is! calculated! by!
subtracting! the! SCP! (p0)! from! the! end! effector! position! (p1),! therefore! x! =! p1!–! p0!
(Assuming! p0!and! p1! are! in! Euclidian! dimensions).! The! constant! k! is! defined! for!
every!object!before!the!interaction!and!the!stiffness!force!is!calculated!dynamically!
as!the!end!effector!moves!inside!the!virtual!object!opposing!the!direction!of!motion!
(see!Figure!27).!!
Rendering!of!stiffness!can!be!done!by!using!the!hlMaterial()!function.!This!function!
is! part! of! the! HL! library! of! the! OpenHaptics! Toolkit! [92]! that! comes! with! the!
Geomagic®!Touch™!FFD.!With!hlMaterials(),!a!function!that!comes!with!the!API,!a!
programmer! can! very! easily! set! haptic! properties! on! virtual! object! by! simply!
stating! the! desired! attribute! and! physical! constants.! An! example! of! using! this!
function!for!setting!the!stiffness!can!be!seen!below:!!
hlMaterialf(HL_FRONT_AND_BACK,!HL_STIFFNESS,!0.7);!
After!applying!this!function!as!seen!above,!the!object!will!be!haptically!visible4!both!
from!the!front!and!the!back!side,!and!the!haptic!attribute!of!stiffness!is!added!with!a!
Hooke’s!Law!constant!of!0.7!N/mm.!Therefore!the!force!produced!will!be:!F=0.7!*!x,!
where!x!is!the!distance!from!the!SCP!to!the!endGeffector!position!(see!Figure!27).!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
4!Haptically!visible!is!defined!as!a!surface!that!provides!haptic!feedback!when!the!cursor!comes!in!
contact!with!it.!
Figure!27!Rendering!of!stiffness!using!Hooke’s!law!
Haptic!
cursor! SCP!
(p0)!
p1!
x!
Virtual!
Object!
In!the!“real!world”!this!opposition!to!the!direction!of!motion!is!similar!to!the!one!
explained!above!until!a!maximum!value!of!x!is!reached,!where!no!more!penetration!
is!allowed!into!the!(assuming!the!object!does!not!break!or!is!punctured).!!
On!the!other!hand,!when!dealing!with!virtual!environments,!the!maximum!force!the!
FFD!can!produce!limits!this!interaction.!The!limits!of!an!FFD!can!mean!they!make!
the!virtual!objects!feel!less!stiff!(softer)!than!they!actually!are,!just!because!they!are!
unable!to!produce!the!necessary!force!to!match!the!user!input.!Geomagic®!Touch™!
for! example! has! a! limit! of! around! 3.3N! [89].! Beyond! that,! the! objects! may! feel!
“springy”,!or!even!in!some!cases,!going!above!this!value,!may!cause!the!device!to!
overheat!and!switch!of!as!a!precautionary,!builtGin!safety!feature.!
6.3.2 Rendering of Surface Texture
There!is!a!number!of!ways!the!surface!texture!can!be!altered!in!the!haptic!virtual!
environment.! A! virtual! object! for! example! can! be! rendered! having! a! virtual!
“physical”!microGtexture,!with!raised!elements,!simulating!texture!in!a!similar!way!
as!in!the!real!world!(e.g.![2]).!The!perception!for!roughness!can!then!be!altered!by!
changing! different! attributes! of! that! microGtexture! as! explained! in! Section! 4.1.4!
Materials!with!ridges!and!grooves,!page!37!(i.e.!altering!grooveGland!width,!element!
spacing!etc.).!!
Another! way! of! simulating! surface! texture! for! psychophysical! experiments!
examining!roughness!perception!is!by!using!a!friction!model![10].!Even!though!a!
number! of! friction! models! exist! (! [10],! page! 190G193),! for! the! purpose! of! this!
project,!surface!texture!was!simulated!using!stickGslip.!!
StickGslip!can!be!described!as!surfaces!alternating!between!sticking!to!each!other!
and! sliding! over! each! other,! with! a! corresponding! change! in! the! force! of! friction.!
Typically,!the!static!friction!coefficient!(a!heuristic!number)!between!two!surfaces!
is!larger!than!the!dynamic!friction!coefficient.!If!an!applied!force!is!large!enough!to!
overcome! the! static! friction,! then! the! reduction! of! the! friction! to! the! dynamic!
friction! can! cause! a! sudden! jump! in! the! velocity! of! the! movement.! Figure! 28!
describes!how!stickGslip!works.!
F!is!the!force!applied!and!D!is!a!drive!system!used!for!controlling!a!virtual!spring.!
The!user!supplies!this!force!during!the!interaction.!S!is!the!elasticity!in!the!system,!
and! M! is! the! load! (cursor! in! our! case,! with! a! weight! equal! to! the! force! the! user!
applies!perpendicular!to!the!object’s!surface)!that!is!lying!on!the!object!surface!and!
is! being! pushed! horizontally.! When! the! drive! system! is! started! (stage! (a)),! the!
spring! S! is! loaded! and! its! pushing! force! against! load! M! increases! until! the! static!
friction!coefficient!between!the!load!M!and!the!surface!in!contact!is!no!longer!able!
to! hold! the! load! anymore.! The! load! starts! sliding! and! the! friction! coefficient!
decreases!from!its!static!value!to!its!dynamic!value!(and!from!“stick”!to!“slip”).!At!
this! moment! the! spring! can! give! more! power! and! accelerates! M! (b).! During! M’s!
movement,!the!force!of!the!spring!decreases,!until!it!is!insufficient!to!overcome!the!
dynamic! friction.! From! this! point,! M! decelerates! to! a! stop.! The! drive! system!
F!
D!
D!
M!
M!
Object!Surface!
Object!Surface!
! F!
F!
S!
S!
(a)!
(b)!
D! M!
Object!Surface!
(a)!
Figure!28!Graphical!representation!of!the!stick:slip!
motion!
however!continues,!and!the!spring!is!loaded!again,!going!back!to!stage!(a),!ready!to!
repeat!the!process.!!
This!constant!sticking!and!slipping,!causes!the!user!to!perceive!this!motion!as!being!
equivalent!to!the!motion!over!a!textured!surface,!giving!the!perception!of!a!“rough”!
surface.!
Using! a! friction! model! to! simulate! “roughness”! was! also! validated! by! a! previous!
experiment!(see![93])!in!which!a!number!of!participants!were!asked!to!manipulate!
three!haptic!attributes!of!a!virtual!haptic!object!and!try!to!replicate!haptically!a!real!
object!in!the!virtual!environment.!These!haptic!attributes!were!the!virtual!object’s!
static!friction,!dynamic!friction!and!stiffness,!but!the!participants!did!not!know!how!
these! properties! were! labelled;! they! just! knew! them! as! A,! B! and! C.! During! the!
debriefing!session,!when!the!participants!were!asked!what!they!thought!they!were!
changing! when! they! changed! the! static! friction,! the! majority! of! them! responded!
that! they! thought! they! were! changing! the! object’s! surface! “roughness”! (meaning!
how! rough! the! object! felt).! More! specifically,! 12/24! participants! described! it!
directly! as! “roughness”,! 5/24! as! “bumpiness”,! 1/24! as! “texture”! and! 1/24! as!
“smoothness”,!which!is!the!direct!opposite!of!“roughness”![56]!(See!Figure!29).!
!
!
Figure! 29! Qualitative! data! describing! how! participants!
perceived! the! rendered! static! friction! from! the! Geomagic®!
Touch™!force!feedback!device.!
!
0!
2!
4!
6!
8!
10!
12!
14!
Qualitative!data!for!Static!Friction!
Therefore,!based!on!the!evidence!gathered,!the!ease!of!implementation,!as!well!as!
the!fact!the!Geomagic!Touch!API!provides!an!easy!and!intuitive!way!of!dynamically!
changing! and! handling! the! static! and! dynamic! friction! models! of! an! interaction!
between! two! objects,! stickGslip! was! chosen! for! simulating! surface! texture! in! the!
experiments!described!in!this!project,!keeping!the!value!of!dynamic!friction!to!0.0!
so!that!it!will!not!interfere!with!static!friction.!